Fluid driven fractures propagate in the upper earth crust either naturally or in response to engineered fluid injections. The quantitative prediction of their evolution is critical in order to better understand their dynamics as well as to optimize their creation. We present a Python implementation of an open-source hydraulic fracture propagation simulator based on the implicit level set algorithm originally developed by Peirce & Detournay (2008) -- "An implicit level set method for modeling hydraulically driven fractures". Comp. Meth. Appl. Mech. Engng, (33-40):2858--2885. This algorithm couples a finite discretization of the fracture with the use of the near tip asymptotic solutions of a steadily propagating semi-infinite hydraulic fracture. This allows to resolve the multi-scale processes governing hydraulic fracture growth accurately, even with relatively coarse meshes. We present an overview of the mathematical formulation, the numerical scheme and the details of our implementation. A series of problems including a radial hydraulic fracture verification benchmark, the propagation of a height contained hydraulic fracture, the lateral spreading of a magmatic dyke and the handling of fracture closure are presented to demonstrate the capabilities, accuracy and robustness of the implemented algorithm.

中文翻译：

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PyFrac：平面 3D 水力压裂模拟器

流体驱动的裂缝自然地或响应于工程流体注入在地壳上层传播。为了更好地了解它们的动态以及优化它们的创造，对其进化的定量预测至关重要。我们基于最初由 Peirce & Detournay (2008) 开发的隐式水平集算法提出了开源水力压裂扩展模拟器的 Python 实现——“一种用于模拟液压驱动裂缝的隐式水平集方法”。比较 冰毒。应用程序 机械。英，(33-40)：2858--2885。该算法将裂缝的有限离散与稳定传播的半无限水力裂缝的近端渐近解相结合。这允许准确地解决控制水力压裂生长的多尺度过程，即使网格相对较粗。我们概述了数学公式、数值方案和我们实现的细节。提出了一系列问题，包括径向水力裂缝验证基准、高度包含的水力裂缝的传播、岩浆岩脉的横向扩展和裂缝闭合的处理，以证明所实现算法的能力、准确性和鲁棒性。